Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJul 22nd 2021
   • (edited Jul 22nd 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded this remark: > Under the [[formal duality]] between [[L-∞ algebras|$L_\infty$-algebras]] and their [[Chevalley-Eilenberg algebra|Chevalley-Eilenberg]] [[dgc-algebras]], [[connective]] nilpotent $L_\infty$-algebras correspond [[bijection|bijectively]] to the connected [[Sullivan models]] ([Berglund 2015, Thm. 2.3](https://ncatlab.org/nlab/show/nilpotent+L-infinity+algebra#Berglund15)). and pointer to * [[Alexander Berglund]], _Rational homotopy theory of mapping spaces via Lie theory for $L_\infty$ algebras_, Homology, Homotopy and Applications, Volume 17 (2015) Number 2 ([arXiv:1110.6145](https://arxiv.org/abs/1110.6145), [doi:10.4310/HHA.2015.v17.n2.a16]( http://dx.doi.org/10.4310/HHA.2015.v17.n2.a16)) <a href="https://ncatlab.org/nlab/revision/diff/nilpotent+L-infinity+algebra/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/nilpotent+L-infinity+algebra/3">v3</a>, <a href="https://ncatlab.org/nlab/show/nilpotent+L-infinity+algebra">current</a>

   added this remark:

   Under the formal duality between $L_\infty$-algebras and their Chevalley-Eilenberg dgc-algebras, connective nilpotent $L_\infty$-algebras correspond bijectively to the connected Sullivan models (Berglund 2015, Thm. 2.3).

   and pointer to

   • Alexander Berglund, Rational homotopy theory of mapping spaces via Lie theory for $L_\infty$ algebras, Homology, Homotopy and Applications, Volume 17 (2015) Number 2 (arXiv:1110.6145, doi:10.4310/HHA.2015.v17.n2.a16)

   diff, v3, current